Inequalities for quantum skew information

Details Inequalities for quantum skew information Inequalities for quantum skew information

2008-03-07

arxiv.org/abs/0803.1056v2

Lett. Math. Phys. (2008) 85:135-146

Physics

Mathematical Physics

Scientific paper

10.1007/s11005-008-0269-0

We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations. Key words and phrases: Quantum covariance, metric adjusted skew information, Robertson-type uncertainty principle, operator monotone function, Wigner-Yanase-Dyson skew information.

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